The SFP method proposed is an alternative to the discrete material optimization (DMO) approach developed. Both approaches are an extension of the multiphase topology optimization. Here, SFP is used to ... [more ▼]

The SFP method proposed is an alternative to the discrete material optimization (DMO) approach developed. Both approaches are an extension of the multiphase topology optimization. Here, SFP is used to select composite plies in a set of candidate orientations, in a formulation including ontinuous design variables. [less ▲]

More than 15 years after the seminal work by Bendsøe and Kikuchi, topology optimization of structures has taken advantage of my research efforts and has now become a commercial available tool (e.g ... [more ▼]

More than 15 years after the seminal work by Bendsøe and Kikuchi, topology optimization of structures has taken advantage of my research efforts and has now become a commercial available tool (e.g. OptiStruct by Altair, Topol by Samtech, etc.). These software tools are daily used in automotive industry and provide engineers with a rational tool for preliminary design of efficient structural components. This paper presents the status of available topology optimization tools and introduces the recent developments that extend their capabilities in order to handle stress constraints, manufacturing constraints, etc. The communication also presents a novel approach of generalized shape optimization that has been introduced to circumvent the difficulties of parametric shape optimization and to complement topology optimization. The approach is based on the eXtended Finite Element Method (XFEM) and the Level Set Description of the geometry. The Level Set description introduces smooth curve descriptions and allows modifying the connectivity of the wholes. The XFEM works with a fixed mesh as in topology optimization, which makes the method very convenient for engineers. Thus the novel approach is likely to bring the next future evolution of structural optimization. Impressive capabilities of this new generation approach will be demonstrated. Application examples from automotive and aerospace engineering will illustrate the different possibilities offered by two approaches. [less ▲]

This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflatable space structures. Although the Newton ... [more ▼]

This paper describes the development of an augmented Lagrangian optimization method for the numerical simulation of the inflation process in the design of inflatable space structures. Although the Newton-Raphson scheme was proven to be efficient for solving many nonlinear problems, it can lead to lack of convergence when it is applied to the simulation of the inflation process. As a result, it is recommended to use an optimization algorithm to find the minimum energy configuration that satisfies the equilibrium equations characterizing the final shape of the inflated structure subject to an internal pressure. On top of that, given that some degrees of freedom may be linked, the optimum may be constrained, and specific optimization methods for constrained problems must be considered. The paper presents the formulation and the augmented Lagrangian method (ALM) developed in SAMCEF Mecano for inflatable structures analysis problems. The related quasi-unconstrained optimization problem is solved with a nonlinear conjugate gradient method. The Wolfe conditions are used in conjunction with a cubic interpolation for the line search. Equality constraints are considered and can be easily treated by the ALM formulation. Numerical applications present simulations of unconstrained and constrained inflation processes (i.e., where the motion of some nodes is ruled by a rigid body element restriction and/or problems including contact conditions). [less ▲]

The design problem consists in maximizing the pull-in voltage using topology optimization method, which is formulated as an optimal material distribution. In addition to the classical volume constraint ... [more ▼]

The design problem consists in maximizing the pull-in voltage using topology optimization method, which is formulated as an optimal material distribution. In addition to the classical volume constraint, different structural constraints could be taken into consideration. Sensitivity analysis is one of the key issues of the optimization process and is performed with the formulation of eigenvalue topology optimization problems. Here the paper investigates topology optimization of strongly coupled electromechanical systems. To avoid important modifications of the electric field by the optimization process, this first study considers a non design electrode and use topology optimization to design an optimal suspension structure. Solution procedure of the optimization problem is based on CONLIN optimizer using a sequential convex programming. This method that has proved its efficiency in many structural problems (sizing, shape) is here tailored to strongly coupled multiphysics design problems under consideration. The choice of appropriate explicit convex approximations schemes for multiphysic problems is investigated. The proposed method is illustrated and validated on microbeam optimization applications. [less ▲]

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended ... [more ▼]

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization. [less ▲]

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended ... [more ▼]

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization. [less ▲]

The structural design of fixtures for vibration testing of structures on electro-dynamic shakers correspond to a constrained optimization problem. The design methodology proposed in this paper is based on ... [more ▼]

The structural design of fixtures for vibration testing of structures on electro-dynamic shakers correspond to a constrained optimization problem. The design methodology proposed in this paper is based on topological optimization tools. It is illustrated on industrial application examples such as the vibration testing of a space mirror and a street lighting device. [less ▲]

in Herskowitz, José (Ed.) Proceedings of the 6th World Congress of Structural and Multidisciplinary Optimization (WCSMO6) (2005, May)

This paper describes a first step work devoted to applying XFEM and Level Sets methods in optimization of structures. This first step work is based on integrating an existing XFEM code within a general ... [more ▼]

This paper describes a first step work devoted to applying XFEM and Level Sets methods in optimization of structures. This first step work is based on integrating an existing XFEM code within a general open optimization tool, SAMCEF BOSS QUATTRO. Unlike most of the existing works, this approach is more shape optimization oriented. A library of pre-formatted basic geometric entities (such as ellipses, squares, triangles, etc.) described by Level Sets functions are used. These basic Level Set features can be combined to represent many kinds of interfaces and holes. The construction parameters of the basic Level Sets are considered as the design variables. In order to evaluate the sensitivities, a finite difference scheme over the design variables is used in this first work. Different mechanical responses (energy, weight, displacement, . . .) can be considered as objective functions or constraints in the problem formulation. Several academic 2D test cases of shape and topology optimization are presented within the XFEM and Level Set approach. In addition, a work by Missoum et al. [11], in which the shape and topology optimization of the structure is carried out by an optimal selection of holes characteristics with a genetic algorithm is presented. [less ▲]

This paper proposes a new first-order approximation scheme used for solving structural optimization problems. It is based on approximations of the MMA family (MMA and GCMMA), but it utilizes the gradients ... [more ▼]

This paper proposes a new first-order approximation scheme used for solving structural optimization problems. It is based on approximations of the MMA family (MMA and GCMMA), but it utilizes the gradients and/or the function values at two successive design points to improve the quality of the approximation. In addition, this scheme can consider simultaneously monotonous and nonmonotonous structural behaviour. According to the characteristics of the treated problem, one of the approximations or a mix of them is automatically selected. Based on this approach, the accuracy of the approximated subproblems is improved and the solution process can be sped up. Numerical results compare the effectiveness of the method with previously derived approximations of the MMA family for shape optimization of trusses and for composite design problems. The benefit of using mixed approximations is also discussed. [less ▲]

The design of composite structures is considered here. The approximation concepts approach is used to solve the optimization problem. The convex approximations of the MMA family are briefly described ... [more ▼]

The design of composite structures is considered here. The approximation concepts approach is used to solve the optimization problem. The convex approximations of the MMA family are briefly described. Several modifications of these approximations are presented. They are now based on gradient information at two successive iterations, avoiding the use of the expensive second-order derivatives. A two-point fitting scheme is also described, where the function value at the preceding design point is used to improve the approximation. Numerical examples compare these new purely non-monotonous schemes to the existing ones for the selection of optimal fibers orientations in laminates. It is shown how these two-point based approximations are well adapted to the problem and can improve the optimization task, leading to reasonable computational efforts. A procedure is also derived for considering simultaneously monotonous and non-monotonous structural behaviors. The resulting generalized approximation scheme is well suited for the optimization of composite structures when both plies thickness and fibers orientations are considered as design variables. It is concluded that the newly developed approximation schemes of the MMA family are reliable for composite structures optimization. All the studied approximations are convex and separable: the optimization problem can then be solved using a dual approach. (C) 2002 Civil-Comp Ltd and Elsevier Science Ltd. All rights reserved. [less ▲]